It seems that your Jane Watson was the daughter of John and Elizabeth Watson who were living at Westgate, Rotherham in 1841 & 1851. I checked in the Rotherham All Saints baptism index and found the following children of John & Elizabeth Watson:
Robert, bap 6 Mar 1836. Mary Ann, born 9 Jul 1838 bap 5 Aug 1838. Betsy Clara, born 7 Apr 1840 bap 20 Jan 1841. JANE, born 28 Dec 1841 bap 7 Feb 1841 (sic), (I think the baptism year should be 1842). Thomas, born 20 Mar 1844 bap 5 May 1844. Sarah Ann, born 11 Nov 1846 bap 25 Dec 1846.
In 1841 the family are living at Westgate, Rotherham. Ref: Piece 1332/book 13/folio 36/page 12.
In 1851 they are still at Westgate Rotherham. Ref: Piece 2343/folio 347/page 24. On ANCESTRY the surname has been mis-transcribed as WALSHE, which is probably why you haven't found them yourself.
In 1861 John Watson, widower, is living at No 32 Orchard Yard, Kimberworth with two of his daughters: Sarah Ann 16, and Elizabeth 9. Next door at No 33 is Samuel Woodhouse with wife Jane and son Henry. Ref: Piece 3506/folio 69/page 16.
Hope this helps,
Patrick